Our DMRG results suggest that the itinerant electrons in the rare-earth \(5d\)  orbital play a vital role in leading the ground state of the two-band Hubbard model to behave distinctly from the single-band Hubbard model at half-filling. Surprisingly, we have seen nearly “half-filled" charge stripes in the Ni layer even at half-filling. The possibility remains that manipulating the model parameters, such as the on-site energy difference, may enhance the SC pair-pair correlation function in the Ni layer, leading to form the LE liquid alternatively at half-filling.
For hole doping level at \(\delta =12.5\%\) , the two-band Hubbard model resembles the single-band Hubbard model since the rare-earth \(5d\)  band becomes almost empty. This interplay between the itinerant rare-earth \(5d\)  electrons and the Ni \(3d_{x^2-y^2}\)  orbital coincides with the experimental observation that \(5d\)  electron pocket diminishes and the \(3d\)  hole pocket becomes dominating when the doping level is increased to approximately \(12\%\) , where the SC dome starts to emerge [1]}, [2]}, [3]}, [4]}. Our DMRG results at \(\delta =12.5\%\)  may also explain the similarity of the phase diagram between the infinite-layer nickelates and cuprates at the overdoping range and why the SC dome of infinite-layer nickelates ends at \(\delta \approx 25\%\) , a typical value for cuprates.
